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Find the value of n if 2/3 to the power of 3 ×2/3 to the power of 5 =2/3 to the power of n-2 |
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Answer» ong>Step-by-step EXPLANATION: The VALUE of n is 10. Step-by-step explanation: Given : Expression (\frac{2}{3})^3\times (\frac{2}{3})^5=(\frac{2}{3})^{n-2}( 3 2
) 3 ×( 3 2
) 5 =( 3 2
) n−2
To find : The value of n in each of the following expression ? Solution : Expression (\frac{2}{3})^3\times (\frac{2}{3})^5=(\frac{2}{3})^{n-2}( 3 2
) 3 ×( 3 2
) 5 =( 3 2
) n−2
Using exponent identity, a^b\times a^C=a^{b+c}a b ×a c =a b+c
(\frac{2}{3})^{3+5}=(\frac{2}{3})^{n-2}( 3 2
) 3+5 =( 3 2
) n−2
(\frac{2}{3})^{8}=(\frac{2}{3})^{n-2}( 3 2
) 8 =( 3 2
) n−2
Comparing the base, 8=n-28=n−2 n=10n=10 Therefore, the value of n is 10. #Learn more 2^n= 512 find the value of n in each of the following |
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